# Find a weak learner in Boosting

I know gradient boosting use an iteration approach to finding a weak learner. But I am confused about the way to find weak learner, PDF source

Question 1:

Why find the weak learner by the formula in the blue box?

Question 2:

What the meaning of the formula $w_ih(\mathbf x_i)$?

Question 3:

In the green box, I think the formula is to calculate the gradient, but how can I understand - before the formula?

• Quick edit, Boosting is not a greedy approach to find weak learner but start with a weak learner and iterate over it (over-sample mis-classifieds data, -> retrain -> update the weights -> repeat until convergence) – Nishad Jul 20 '18 at 3:45
• The principle idea of gradient boosting is to make the weak learner at each iteration pointing to the direction of negative gadient of the current loss with respect to the current ensemble. Understanding this idea could make the equations straightforward. – doubllle Jul 20 '18 at 15:33
• @Nishad Sorry, I have edited it! – Lei Chen Jul 21 '18 at 7:26